reference request – A $p$-adic homotopy theory for non-simply connected spaces? Answer

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reference request – A $p$-adic homotopy theory for non-simply connected spaces?

I’m looking to understand the state of the art for $p$-adic (unstable) homotopy theory of non-simply connected (non-nilpotent!) spaces. Ideally, I’d also like integral versions, eg things like Mandell and Yuan’s theorems, but without any restriction on fundamental group (the spaces I care about are all $K(\pi,1)$s). Squinting at the rational homotopy theory literature in the non-simply connected case (e.g. Brown-Szczarba, or Gomez-Tato-Halperin-Tanre), I can imagine that what I want may be “known to experts”, in which case pointers toward that, or precise statements of what’s expected are most appreciated. Thanks!

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